Question 1121117
<br>
The given ratios are<br>
A:L = 8:15
L:S = 5:8
S:J = 4:5<br>
To compare the shares of all 4 of them, multiply the ratios by constants as appropriate to get the same numbers for the same people.<br>
For example, for S we have<br>
A:L = 8:15  and  L:S = 5:8<br>
Multiply the second ratio by 3 so that "L" is 15 in both:<br>
A:L = 8:15  and  L:S = 15:24<br>
Then we know<br>
A:L:S = 8:15:24<br>
Now we have<br>
L:S = 15:24  and S:J = 4:5<br>
Multiply the second ratio by 6 so that "S" is 24 in both:<br>
L:S = 15:24  and S:J = 24:30<br>
So now we know<br>
L:S:J = 15:24:30<br>
Put it all together and we have<br>
A:L:S:J = 8:15:24:30<br>
So the portion of the rent that Samson will pay is 24/(8+15+24+30) = 24/77.